An efficient finite element solution of water infiltration in variably saturated soils

The convergence difficulty associated with solving the non-linearity of the Richards's equation is often encountered in numerical simulation of infiltration into dry soils driven by gravity. In previous work we proposed a simple approach to solve the gravity term for one-dimensional infiltration, and test on a wide range of problems shows considerable improvement over the existing Picard and Newton methods. The purpose of this note is to explain how to extend the method to multi-dimensional finite element solution and demonstrate its superiority to the standard Picard and Newton methods.